Pat Howard scored the crucial try, his second of the campaign, but Jones felt his troops were not at their best.
And with a tough clash against Munster coming up, Jones has warned that the team will have to be much-improved for their second home game of the season.
"I went in the changing room afterwards and tried to be positive, because we won a game and it should give us some confidence for Munster next week," said Jones.
"We had everything to lose and nothing to gain against Zebre, but we have to be a lot better than that.
"I am disappointed for the fans because I really wanted to start well and give them something to cheer for the 80 minutes.
"Now we go into a game against Munster when not many people will give us a chance and we just have to move on and look forward.
"I have to see the positives but there is no hiding away from that not being what we wanted and we have to be a lot better."
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